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BASICS OF COMPUTER APPLICATIONS
ASB 102
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UNIT 1Introducing computer system
Number systemWhat is number system?Types of number system Their ConversionsBinary arithmetic ( addition, subtraction,
multiplication )
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Number system
• In any number system there is an ordered set of symbols known as DIGITS with rules defined for performing arithmetic operations like +, - , * etc
• A collection of these digits makes a number which in general has two parts -
1) integer
2) fractional
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Set apart by a radix point (.)
• (N)b = dn-1 dn-2….di….d1 d0 . d-1 d-2…d-f….d-m
Integer portion radix fractional portion
Where
N – number
B – radix or base of the number system
n – number of digits in integer portion
m- number of digits in fractional portion
Dn-1 - most significant digit (msd )
D-m - least significant digit ( lsd )
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Types of number system
• Binary number system
• Octal number system
• Decimal number system
• Hexadecimal number system
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1. Binary number system
• Have base/radix 2 (two)
• Only two symbols are used to represent binary number system 0 and 1
• Eg 1011.11
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2. Decimal number system
• Have base 10
• Symbols- 0,1,2,3,4,5,6,7,8,9
• Eg- 3974.57
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3. Octal number system
• Have base or radix eight
• Symbols used to represent numbers- 0,1,2,3,4,5,6,7
• Eg- 3567.25
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4. Hexadecimal number system
• Have base 16 which requires 16 distinct symbols to represent the numbers.
• Symbols used are 0 through 9 and alphabets A and f.
• This is an alphanumeric number system.
• Eg- 3FA9.56
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Conversions - Decimal to binary
Eg1 (13)10 to ( ?)2
quotient remainder
13/ 2 6 1
6/2 3 0
3/2 1 1
½ 0 1
Thus (13)10 = ( 1101)2
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• Eg ( 10.625)10 to ( ?)2
(10)10 - 1010
0.625 * 2 =1.250 1
0.250* 2 = 0.500 0
0.500* 2 = 1.000 1
101
( 10.625)10 to (1010.101)2
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Conversion – binary to decimal
• eg- 110101.101
= (1*25) + (1*24) + (0*23) + (1*22) + (0*21) + (1*20) + (1*2-1) + (0*2-2) +(1*2-3)
=32 + 16 + 0 + 4 + 0 + 1
= ( 53)10